ca_m11 - MAC 1105 Module 11 Solution of Polynomial...

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Rev.S08 MAC 1105 Module 11 Solution of Polynomial Equations
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2 Rev.S08 Learning Objective Upon completing this module, you should be able to: 1. Solve polynomial equations using factoring. 2. Solve polynomial equations using factoring by grouping. 3. Solve polynomial equations using the root method. 4. Find factors, zeros, x-intercepts, and solutions. http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
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3 Rev.S08 Quick Review of Polynomial Division http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. The The quotient quotient is is x 2 + 5 + 5 x + 10 with a + 10 with a remainder remainder of 24. of 24. Check:
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4 Rev.S08 Division Algorithm for Polynomials http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
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5 Rev.S08 Remainder Theorem and Factor Theorem http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
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6 Rev.S08 Example Use the graph of f ( x ) = x 3 - x 2 – 9 x + 9 and the factor theorem to list the factors of f ( x ). Solution The graph shows that the zeros or x -intercepts of f are - 3, 1and 3 . Since f ( - 3) = 0, the factor theorem states that ( x + 3) is a factor , and f (1) = 0 implies that ( x - 1) is a factor, and f (3) = 0 implies ( x - 3) is a factor . Thus the factors are ( x + 3)( x - 1), and ( x - 3) . http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
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7 Rev.S08 Complete Factored Form http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
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8 Rev.S08 Example http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Find all real solutions to the equation 4 x 4 – 17 x 2 – 50 = 0. Solution The expression can be factored similar to a quadratic equation . The only solutions are since the equation x 2 = –2 has no real solutions.
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9 Rev.S08 Another Example http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
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